The Monte Carlo Approach to State Estimation for Linear Dynamical Systems with State-Dependent Measurement Noise

Abstract

This paper is concerned with the state estimation of linear dynamical systems with state-dependent measurement noise. The minimum variance estimate of the state is obtained as the weighted mean of the outputs of Kalman filters parameterized by the state-dependent measurement noise sequences. The usual calculation for this estimate, however, becomes impractical since a very large amount of outputs of Kalman filters is required. Therefore, we regard the set of all the state-dependent measurement noise sequences as a population. Then, we evaluate the minimum variance estimate on the basis of a relatively small number of outputs of Kalman filters, parameterized by the state-dependent measurement noise sequences sampled at random from the population. The convergence of the algorithm is established. Then, by an approximation of a sampling procedure with a fast convergence property, a feasible sampling procedure is determined and a practical algorithm is designed. This policy of design leads to an efficient algorithm. Digital simulation results show a good performance of the proposed algorithm.